NBSIR 73-404

Mass Transport and Physical Properties of

Large Crystals of Calcium Apatites:

Studies of CajOHl^ Crystals for use in

Electrolytic Conversion of Calcium Fluorapatite

Crystals to Calcium Hydroxyapatite

A. D. Franklin and K. F. Young

Inorganic Materials Division

Institute for Materials Research

National Bureau of Standards J

Wasfiington. D. C. 20234 ^

September 1. 1972 • August 31. 1973

Annual Report

Prepared for Department of Health. Education, and Welfare

National Institutes of Health

National Institute of Dental Research

Bethesda, Md. 20014

Interagency Agreement No. YOl-DE-SOOlO

NBSIR 73-404

MASS TRANSPORT AND PHYSICAL PROPERTIES OF

LARGE CRYSTALS OF CALCIUM APATITES:

STUDIES OF Ca(0H)2 CRYSTALS FOR USE IN ELECTROLYTIC CONVERSION OF CALCIUM FLUORAPATITE

CRYSTALS TO CALCIUM HYDROXYAPATITE

A. D. Franklin and K. F. Young

Inorganic Materials Division

Institute for Materials Researcti

National Bureau of Standards

Washington, D. C. 20234

September 1, 1972 - August 31, 1973

Annual Report

Prepared for Department of Health, Education, and Welfare

National Institutes of Health

National Institute of Dental Research

Bethesda, Md. 20014

Interagency Agreeme.nt No. YOl-DE-30010

U. S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS. Richard W. Roberts. Director

ABSTRACT

In order to convert single crystals of calcium fluorapatite to

calcium hydroxyapatite , an electrolytic cell technique will be explored.

To utilize such a technique, the cathode compartment must consist of a

source of hydroxyl ions and a barrier to the flow of all others. Excunination

of the literature on metallic hydroxides suggests that a suitable cathode

might be composed of an oriented MeCOH)^ crystal, where Me is Mg, Ca,

Sr, or Ba, backed up by a Pt electrode in an atmosphere containing H^O

and O^. CaCOH)^ crystals have been grown from aqueous solution, and Pt

electrodes evaporated onto them. An apparatus has been built to study

their ac admittance as a function of temperature and atmosphere, and

measurements begun. A computer program for handling the complex admittance

data has been devised and tested.
- 2 -

1. INTRODUCTION

Large crystals of calcium hydroxyapatite, (Ca^^ (PO^) ^ (OH) or OHAp)

have not yet been grown synthetically, although somewhat impure natural

crystals do exist. On the other hand, large crystals of the closelyrelated calcium fluorapatite

(*-^]^o ^^"^4^ 4^2 ' ^^P) calcium chlorapatit<

(Ca^Q (PO^) ^Cl^ , or ClAp) have been grown by the Kyropoulos method (Johnson,

1961) , from a flux composed of the corresponding Ca halide (Prener, 1967)

,

and by the Czochralski method (Mazelsky et. al., 1968). All three apatites;

have closely-related crystal structures (Young, 1967) and the X ions in

XAp are known to be relatively mobile (Tse et. al., 1972a). This suggests

that perhaps large crystals of OHAp can be prepared by replacing F in

FAp or CI in ClAp crystals by OH .

Indeed, Young and Elliot (1966) have succeeded, by annealing ClAp in

steam at 1000°C, in replacing all but about 6% of the CI with OH ions.

However, such a diffusion-controlled process would produce a flux of CI

ions out of the crystal, and OH ions in, that would eventually decrease

exponentially with time, and would therefore take an almost infinite

amount of time to replace the last traces of Cl ions with OH ions.

This difficulty could be obviated by using an electrolytic technique,

" in which an electric field is applied to drive out the F or Cl and drive

in the OH ions. The field would impose the same drift velocity on all ionj

of the same kind, which in a large field can be much greater than the diffu

random-walk velocity. An approximate calculation, given in the Appendix,
- 3 -

suggests that complete replacement of all F ions might be accomplished

3 at about 380°C in a few days under an applied field of 10 V/cm.

It is therefore the first objective of this project to test the

possibility of the electrochemical trans formation of large single crystals

of FAp to OHAp .

The method to be tried is shown schematically in Figure 1 . An

electrolytic cell will be constructed with the FAp crystal as the

electrolyte, oriented with the applied electric field along the c-axis.

The anode compartment will be composed of a thin crystal of CaF^ plated

v;ith Ca metal or with a pressed mixture of CaF^ and Ca metal, backed

by a Pt electrode. It has been shown (Hinze and Patterson, 1973) that

the transport number of the F ion in CaF^ is unity in the presence of

metallic Ca down to 400°C, and probaibly lower. The conductivity of

oxygen-doped CaF^ (Rossing, 1966) is shown in the Appendix to be

sufficient to allow the desired current to flow.

The first major problem lies with the cathode compartment. A crystal

conducting only by OH ion transport is needed, and while on structural

grounds there are several promising candidates, none is known definitely

at present. The initial task in this work is therefore the selection

of the cathode material. A suitable material will be fitted with

porous electrodes, probably of Pt, capable of catalyzing the reaction

2H^0 +0^+46? 40H~. (1.1)
- 4 -

2. CATHODE MATERIALS

2.1 Literature Study

A crystalline hydroxide of good stability in the temperature

region from 300-500°C is required, in which there is reason to believe

that OH ions exist and are mobile. Among several promising classes

are those with formula MeOOH, where Me stands for Fe or Al , and the

alkaline earth hydroxides with formula Me (OH) 2-

J

2.1.1 MeOOH

, White (1971) reported studying the transport of OH

ions in SiO^, using geothite (FeOOH) as the cathode material for a

determination of the electrical conductivity. However, in a private

communication he stated that there was no independent information on

the transport number and mobility of OH in FeOOH.

The hydroxy oxides of Al and Fe occur with two distinct structures,

that of boehmite (y-AlOOH) or lepidocrocite (y-FeOOH) , and that of

diaspore (a-AlOOH) and goethite (a-FeOOH) , In all four compo\inds , the

shortest distances between oxygen ions not part of the same metal-oxygen

octahedron are about 27 nm, and are assumed (Milligan and McAtee, 1956)

to represent hydrogen bonds. This is consistent with data on the infrared optical absorption of boehmite (Schwartzmann, 1962; Wickersheim and

Korpi , 1965), which exhibit what are probably O-H stretching bands in

the wavelength region from 3000 to 3300 cm ^

. Hydrogen bonds between

two oxygen ions separated by 27 to 27.5 nm generally have their O-H.
- 5 -

stretching frequencies in this region (Pimentel and McClellan, 1960)

2-

The existence of distinct hydrogen bonds between the OH and O

ions suggests that charge transfer might take place by proton motion

rather than by hydroxyl ion motion. If so, this class of materials

would be unsuitable as the cathode compartment material. Fripiat and

coworkers have indeed interpreted measurements with boehmite on the

temperature dependence of the infrared intensities (1967a) , dielectric

absorption, electrical conductivity, and proton diffusion (1967b), and

proton nmr (1969) on this basis. We have, therefore, chosen not to

examine these MeOOH compounds further.

2.1.2 Me (OH)

The situation is quite different with respect to the

alkaline earth hydroxides with the Brucite structure. These crystals

belong in the hexagonal system, with the oxygen ions arranged linearly

o along the £ axis. The smallest 0-0 distance is about 3.3 A in Ca(0H)2

which led Bernal and Megaw (1935) to suggest that no hydrogen bonding

takes place. In Mg(0H)2, and also presumably in Ca(0H)2, the O-H bonds

also lie along the c_ axis (Elleman and Williams, 1956), with an O-H bond

o length of about 0.98 A (Elleman and Williams, 1956; Busing and Levy, 1957;

Henderson and Gutkowsky, 1962) , quite comparable to that in non-hydrogenbonded molecules. The vibration corresponding to the O-H stretching

frequency, while somewhat complex due to mixing with the lattice modes,

occurs (e.g., Buchanan, Gaspers, and Murphy, 1963) around 3700 cm ^, where
- 6 -

it would be expected for non-hydrogen-bonded OH .

It thus appears that Ca(0H)2 should be a reasonable candidate for

an OH conductor, and experiments to grow crystals and determine the

transport number of the OH ion were begun.

Experimental Study of Ca(0H)2

2.2 Crystal Growth

In order to determine the properties of CaCOH)^/ and indeed

to utilize this highly anisotropic substance in the cathode compartment

J of the electrolytic cell for conversion of FAp to OHAp, single crystal

plates are necessary of about 1 mm thickness, along the c axis, and

2 several mm area perpendicular to the c axis

Satisfactory crystals have been grown by the diffusion technique

(Ashton and Wilson, 1927) using an apparatus as shown in Figure 2.

Ca^-free water is used, prepared by boiling distilled water slightly

acidified with HCl for about 16 hours in a reflux condenser. Air first

passed through an ascarite column is slowly bxibbled through the water

during boiling. The U-tube in Figure 2 is filled with this water, under

a protective layer of liquid paraffin, and then NaOH solution, about 27

molar, is carefully pipetted into the bottom of one of the vertical

inner tubes and saturated CaCl^ into the bottom of the other, without

allowing stirring of the water above these solutions. The NaOH and CaCl^

solutions form distinct, quiescent layers below the water, with initially

well-defined interfaces separating them from the water. The NaOH
solution, under paraffin oil, was allowed to stand for at least two days

to let any Na^CO^ settle out. The CaCl^ solution was prepared with CO^-free

water, slightly acidified, and boiled with CO^ free air passing through

it for 16 hours. It was also stored under paraffin oil.

2+ - The crystals grow by interdiffusion of Ca and OH ions. The OH

ions travel much more rapidly in aqueous solution than do the other ions,

as shown by the values given below for the equivalent conductance of

these ions (Chemical Rubber Handbook, 39th Edition)

:

_ * OH 172.0 Siemens

Cl~ 65.5

1/2 Ca^"^ 51.0

Na"^ 43.5.

Without special precautions to inhibit the transport of OH ions, it was

found that the crystals grown (all growth so far has been at room temperature)

2+ were acicular in shape, perhaps due to high concentrations of Ca ions during

growth

.

A satisfactory arrangement has been to restrict the transport of OH

ions by making the orifices (there are four) of the inner tube containing

the NaOH solution small, about 1 mm in diameter, while those of the

CaCl^ are considerably larger. Under these conditions, small plates of

* Siemens is the SI unit for conductance, and equals the previously-used

mho, or reciprocal o\m.
- 8 -

Ca.(OU)'^, several imn across, grow inside the CaCl^ inner tube over a

period of several weeks. As Ca^"*" diffusion reaches the NaOH chamber,

crystallization occurs at the orifice, eventually blocking it. This

effect limits the size of the crystal obtained at present, but they

should be large enough to allow determination of the OH transport in

Ca(0H)2 and to test the feasibility of electrolytic conversion of FAp

to OHAp. The crystals are stored under benzene to protect them from

atmospheric CO^

2.3 Electrode Application

The electrodes to be applied to the CaCOH)^ crystals must serve

a dual purpose. They must not only supply electrons but must also

catalyze the reaction between water, oxygen, and electrons (Eq. 1.1)

to produce hydroxyl ions. Platinxom is known to operate in just this

fashion in both aqueous systems and as electrodes in fuel cells reacting

with (e.g., Hoare, 1968). Some such cells use an alkaline medixim,

such as an aqueous KOH solution and their operation most probably is

very similar to what should occur on our Ca (OH) ^ crystals provided the

OH ions are mobile. Because of this favorable history and because Pt

can be evaporated reasonably readily, it was decided to begin at least

with evaporated Pt electrodes.

Evaporation of Pt electrodes was done in a vacuum, under a pressure

2 ~S of a few N/m (a few mm of Hg x 10 ) , produced by a diffusion pump

operating through a liquid-nitrogen trap. The crystal was placed in a

copper cup, under benzene, and covered with a nickel plate with a hole
- 9 -

approximately 1-1/2 mm in diameter under which the crystal was positioned.

As the vacuum was established the benzene evaporated, leaving the crystal

ready for deposition of Pt through the hole to form a round electroded

area. During evaporation the cup containing the crystal became quite

warm but no serious decomposition of the crystal was immediately apparent.

The course of the evaporation was monitored by following, with an ohmmeter,

the conductance of the film deposited upon a glass surface placed near the

crystal. While this measurement has not yet enabled us to estimate

quantitatively the film thickness, it has been useful as an indicator

of the onset and continuation of deposition. After evaporation, CO^-free

air was admitted to the bell jar, the jar lifted away and benzene

quickly added to the cup, immersing the specimen. The crystal was turned

over and the process repeated, to produce Pt electrodes on each of the

basal faces.

Although no damage to the crystals during deposition was immediately

observable, some of the evaporated electrodes have not been firmly attached

to the crystal, and have become detached after a period of time, more or

less as single units. Contributing factors may be deposition of extraneous

material from the benzene bath (ACS certified benzene, thiophene-free

,

was used and should leave negligible residue) ; surface decomposition of

the crystal, with loss of water, either by infrared heating by the hot

filciment or by bombardment by hot Pt ions; or surface contamination of

the crystal by CO during handling.
- 10 -

2.4 Electrical Measurements

In order to determine that OH ions are the predominant charge

carriers in CaCOH)^ it will ultimately be necessary to compare the total

charge, coulometrically determined, with the total quantity of OH

ions trcinsported in a symmetric dc electrolytic cell. The passage of

OH ions can be monitored by the disappearance of H^O and 0^ from one

side of the cell and their appearance at the other. However, preliminary

measurements are needed to obtain an estimate of the total conductance

of the Ca(0H)2/ to determine whether it is large enough to maintain the

current required for conversion of FAp to OHAp in a reasonable time.

The most useful form of preliminary measurement appears to be an ac

measurement of the capacitance and conductance of the CaCOH)^ crystal,

between Pt electrodes deposited upon each side. At sufficiently high

frequency, the observed values of capacitance and conductance should

be the true values for the crystal, while any blocking of charge carriers

at the electrodes should produce a decrease in conductance and a rise

in capacitance as the frequency decreases (see e.g., Friauf, 1954).

Such measurements, made as functions of H^O and 0^ content of the

atmosphere, could also give information about the proposed catalytic

reaction on the Pt electrodes. The temperature should also be varied

in the search for a range of variables giving satisfactory performance.

2.4.1 Measurement Cell

The first cell built, which used a ceramic specimen holde

proved to be unsatisfactory because of extraneous conduction through
-lithe ceramic holder. The holder shown in Figure 3 was then built, and

appears to be giving satisfactory results.

The inner assembly, shown in Figure 3, is enclosed in an external

stainless-steel can which bolts to the cover plate with an o-ring seal,

so that the atmosphere surrounding the specimen can be controlled. The

electrical leads are fed through the cover plate via insulating seals, and

since these are kept at room temperature, there is negligible conductance

between these leads. The specimen sits upon a silvered Ni plate which

makes contact with the lower evaporated Pt electrode of the specimen (in

future work a path may have to be provided to allow better atmospheric

access to this electrode) . The upper Pt electrode is contacted by a

spring-loaded nichrome wire fastened electrically to the slack Pt lead

wire connecting to the external bridge. The lower portion of the assembly

can be inserted into a controlled furnace and the temperature monitored

by the Pt/Pt-10% Rh thermocouple near the specimen.

The electrical measurements are made using a Wayne-Kerr B221* bridge,

using either the internal oscillator and detector at 1592 Hz or, for

varying frequencies, a Krone-Hite 440 AR oscillator and General Radio

12 32-A tuned amplifier as a detector. The frequency range available

with this arrangement is from about 50 Hz to perhaps 70 kHz, although

the latter figure may be pushing the bridge too far.

*Certain commercial equipment, instruments, or materials are identified in

this paper xn order to adequately specify the experimental procedure. In no

case does such identification imply recommendation or endorsement by the

National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best available for the purpose.
In using the cell, it is necessar" to know the capacitance and conductance shunting the specimen. Since the shunt capacitance is expected

to vary with the length of the central lead, measurements were made,

without a specimen, as a function of the distance between the lower plate

contact and the bottom of the upper wire contact. Figure 4 shows that ^

the shunt conductance is independent of the distance between contacts I

but does depend upon frequency. The shunt capacitance, shown in Figure 5, j exhibits a roughly linear dependence for large separation of the contacts

plus a component that rises rapidly as the separation decreases. This

latter component represents the direct capacitance between the contacts

and will be replaced by the specimen capacitance during the actual measurement. Hence, correction of the experimental data for the shunt capacitance

introduced by the cell requires the linear component only, extrapolated ;|

to a contact separation equal to the specimen thickness.

The frequency dependences of the linear component of the shunt capacitanc^

at three values of the contact separation and of the shunt conductance j

are shown in Figure 6. There is no dependence upon temperature. When !

the bridge is used to measure the equivalent parallel capacitance and I

conductance of the crystal, appropriate numbers from this Figure 6 can be

subtracted from the measured data to yield values for the specimen

alone. For the shunt capacitance, interpolation to the correct specimen

thickness is needed.

2.4.2 Measurements on Crystals

Measurements have been made on two crystals. Due to the

small amount of data obtained as yet, and the evidence for atmospheric
- 13 -

attack upon the specimens, to be discussed, these measurements are only

of a very preliminary nature.

Figure 7 shows equivalent parallel capacitance and conductance

data obtained at 345°C on a Ca(0H)2 crystal in the earlier specimen

holder. Because in this specimen holder the shunt admittances were

large, the values attributable to the specimen are rather uncertain,

particularly the conductance above about 10 Hz. However, a relaxation

appears centered aroiind 600 Hz. These data appeared to be independent

of the atm.osphere, whether dry "CO^-free" air or nitrogen, or ^ir or

nitrogen bubbled through "CO^-free" water held at room or ice temperatures.

A very similar curve was found for a second crystal in the improved

specimen holder described here, held at 335°C in dry "CO^-free" air,

as shown in Figure 8. For both crystals at room temperature, essentially

no equivalent parallel capacitance or conductance was found. The electrode

-2 2 areas are very small, of the order of 10 cm , and the specimen thickness

-2

about 5x10 cm, so that the true capacitance could not have been

greater than about 0.1 pF. The much larger values seen in Figures 7

and 8 undoubtedly arise from the blocking of charge carriers at the

electrodes

During these measurements, and particularly those for the second

crystal. Figure 8, it became apparent that irreversible changes were

taking place in the crystals, and upon subsequent examination they were

found to have undergone extensive attack by CO . The electrical data
- 14 -

may well have been influenced by this attack, and more stringent

precautions in eliminating CO^ from the atmosphere will be required.

2.5 Atmosphere Control

Most of the measurements were made in wet or dry air that had

been passed through a column packed with an NaOH-asbestos mixture, about

15 cm long. This "CO^-free" air when bubbled, via a fine glass frit, through

a saturated solution of Ba(0H)2 for several days produced no visible

precipitate, whereas without the ascarite column a precipitate was formed.

On the other hand, when the "CO^-free" air was passed over Ba (OH) ^ crystals

held at room temperature, attack was soon noted and in a few days the

BaCOH)^ appeared to be completely converted to BaCO^

This apparent great reactivity of the alkaline earth hydroxides in

crystal form is demonstrated by another observation. Ca (OH) ^ crystals

kept under ethyl alcohol exhibited signs of CO^ attack after days or

weeks. Needles were much more rapidly attacked than plates, and in

both cases the faces parallel to the c_ axis seem to be particularly

reactive. In future experiments, tank gases will be used instead of

air, and rigid precautions will be taken to remove and monitor CO .
- 15 -

3. COMPUTER PROGRAM FOR HANDLING DIELECTRIC DATA

The equivalent parallel admittance of a slab specimen with blocking

electrodes is expected in general to be a complex function of frequency,

but under most conditions of experimental interest to be well represented

(c.f., Raleigh, 1968) by a simple Debye-type expression

iwC ,

. Y =

o (1)

p 1+iwR C

o o

where w is 2tt times the frequency, and C^ and R^ are the low-frequency

limit of the capacity and the high-frequency limit of the resistance.

A simple interpretation is that the crystal behaves like an equivalent

circuit with a resistor R in series with a capacitor C , or like a block

o o of conductive material of resistance P.^ between two identical capacitors

of value 2C , representing the blocking electrodes. Charge is stored in each

G

cycle at the electrode-electrolyte interface, and energy lost by the passage

of the current through the resistive material.

When this equivalent parallel admittance is plotted in the complex

plane, a semi-circular arc is obtained with its center on the real axis,

analogous to the Cole-Cole plot (Cole and Cole, 1942) used in treating

dielectric constant data. Bauerle (1969) has shown for experiments with

calcia-stabilized zirconia solid-state electrolytes with porous Pt

electrodes in oxygen atmospheres that several over-lapping arcs appear,

with centers somewhat below the real axis. The several arcs can be

individually attributed to electrode and bulk processes.
- 16 -

At constant temperature Bauerle found that the electrode resistance

decreased with increasing oxygen pressure, behavior that parallels our

expectations for the behavior of our system of Ca(0H)2 with Pt electrodes

in an H^O/O^ atmosphere. The depression of the arcs below the real

axis suggests a small distribution of electrode and bulk process parameter

which plays a role similar to that of the distribution of relaxation

times in the treatment of the dielectric constant (Cole and Cole, 1942)

Experience in this laboratory with disentangling the several overlapping arcs that can appear in treatments of data such as this has

suggested the utility of having a general, numerical method of fitting

the overall data to a sum of the contributions from several separate

mechanisms, each of which alone would produce a single arc. We describe

next a computer-based technique for performing such fits. In electrode

polarization problems, the data would be most apt to produce a pattern

of arcs when plotted in the complex plane of the admittance,

Y(w) = G(w) + iB(w) , (2)

although dielectric relaxation problems would most likely be dealt with

in terms of the complex capacitance

C(w) = e e 'C - e ie"C . (3)

: . O O O O

In these equations, G and B are the conductance and susceptance, the

dielectric constant of free space, e' and e" the real and imaginary
- 17 -

parts of the relative complex dielectric constant, and e C the air ^ o o capacitance. We discuss our data-handling technique in terms of the

complex capacitance, C* = C ' - iC" , C = e e 'C and C" = e 'e"C , ^ o o o o but it can readily be adapted to use with the complex admittance Y,

or any other similar quantity.

An electronic calculator with a plotter attachment and magnetic

tape cassette memory is used in the processing and display of

the data.

These data are collected as functions of frequency, temperature,

and composition of the controlled gaseous environment of the specimen.

The ease, accuracy, and flexibility of graphically displaying these

data in the complex plane not only allows the structure of the data to

be revealed, but also their dependence on temperature and the nature of

the gaseous environments by plotting families of curves on the same

graph. Selected regions of the graphs can be expanded if necessary, and

graphs of a summary nature or for publication purposes can be quickly

prepared. The data are stored on magnetic tape in cassettes and can be

quickly recalled and re-plotted for comparison purposes.

When the specimen exhibits a single charge-storage mechanism obeying Eq. (1)

,

only one arc is produced in the complex plane, and the data can be fitted

to such an arc by minimizing the sum of the squares of the radial deviations

of the data from the arc. From this arc we then obtain the limiting high and

low frequency values of capacitance (C^, C^) , a most probable relaxation time
- 18 -

(t) and two parameters (m and n) representing the distribution of relaxation

times for that mechanism. The process of fitting also reveals the presence

of more than one mechanism should they exist. Each arc, arising from a

single mechanism but with, in general, a distribution of relaxation times,

may be represented by

AC

C* - C = — (4)

°° 1 . n , . m

1+1 (wt)

where: C* = complex capacitance = C'-iC"; AC = - C^; w = angular

frequency. Then

2 2 \ 1/2

(C -C) + C" ^

o I / ^ m

? 2 iC'-C ) + C"

= (wt) e w (5)

and the depression, D, of the center of the arc below the real axis is

^ Ac ^ ^ nTT ,.. D = — Cot — (6)

and the slope of InVI vs £nw is equal to m:

ilnW = m£nT + m£nw (7)

For a relaxation mechanism with a single relaxation time, D is zero and

m is equal to unity.
_ 19 -

If it appears that there are .two or more mechanisms (two or more

superimposed arcs) present, then the dominant one may be fitted by the

least-squares technique described above, and using equation (4) above,

the contribution from that mechanism may be subtracted from the raw data.

The difference constitutes a new set of data which is presumably due to

all other mechanisms and should itself be suitable for the least-squares

fitting procedure just used provided one of the remaining mechanisms

again dominates the rest. If so, the process may be repeated, removing

this second contribution from the raw data, and so on. When all the

data have been fitted, the entire scheme may be repeated any number of

times, to refine the fit. The whole is an iterative process that

converges on the best possible fitted values by eliminating as far as

possible the interference of one mechanism with another. This procedure

works quite well when dealing with such systems as treated in Bauerle's

study of solid electrolyte polarization (Bauerle, 1969)
- 20 -

4. FUTURE PLANS

Several experimental problems need to be solved in order to complete

the study of CaCOH)^ as a potential cathode material, These include the

deposition of reproducible Pt electrodes without cryistal damage and the

provision of an atmosphere without damaging CO^ for electrical measurements

at elevated temperatures.

Once solutions to these problems are in hand, the task of determining

the electrical properties of CaCOH)^ crystals and finding the conditions

under which electrodes reversible to the generation a.nd absorption of OH

ions can operate can proceed. Preliminary experiments have shown that

sizeable Ba (OH) ^ crystals can be formed, so the techniques already set

up can probably be used with little modification to screen Sr(0H)2

and Ba(0H)2 crystals as well, if need be.

If reversible electrode action can be achieved in one of these crystals

that exhibits a satisfactory level of conductivity it will then be necessary

to proceed to determining the OH transport numbers, and beyond that the

experiment to replace F ions in FAp with OH ions to produce OHAp.
- 21 -

5. APPENDIX

5.1 Estimation of the Time to Replace F Ions in FAp With OH Ions,

In the hexagonal crystal structure of FAp, the F ions lie in

chains parallel to the c-axis. The chains intersecting a given basal

plane form a hexagonal pattern.

2 Let N = Niimber of chains per cm of basal plane

cL = Thickness of crystal, or length of chain

3

N = Number of vacant F sites per cm

V

n = Number of vacant F sites per cm of chain

V

r = distance between F sites along the chain

r = distance between chain intersections on the basal

a plane.

Then

N = 2/[/3 r ] c a

n = N /N

v v c

The flux of vaccmcies, and therefore F ions, passing through a given

basal plane along a single chain is

F = n yE

v

where u is the vacancy mobility and E the applied field. The number of
- 22 -

ions in the length L is L/r , so that the time to exchange the entire

length is

LN

L ^ c 2L

L L V /3r r yE

. Lav

The conductivity is given by

a = N ye V

where e is the elementary charge.

The familiar ionic-crystal equation for the mobility y may be

written (Lidiard, 1957)

2

' ""l ^

y = -r-r— vexp (As A) exp(-Ah /kT) kT m m

where k is Boltzmann's Constant, T the Kelvin temperature, v the

vibrational frequency of an ion next to a vacancy, and As^ and Ah^

the entropy and enthalpy of activation for the jxsmp of the neighboring

ion into the vacancy.

Numerical values to put into these formulae can at least be estimated.

Arends et. al . (1968) estimate the number of vacancies per cm"^ in OHAp

19

to be about 10 , and we adopt that for N for FAp also. Prener (1967)
- 23 -

—8 —8

gives r = 3.45x10 cm and r = 9.36x10 cm. A thickness (L) of 1 cm

L a

3 for the crystal and an applied electric field of 10 V/cm will be assvuned.

12 -1

The vibrational frequency v of the F ions must be below about 8x10 sec

("^ 240 cm ^) since Baddiel and Berry (1966) explored the infrared vibrational

spectrum as far down in frequency as 250 cm ^ apparently without finding

the lattice vibrations. Typical values for this frequency (c.f., Donovan

12

and Angress, 1971) in relatively ionic cirystals run from about 2x10

13 -1

to 10 sec . For the purposes of this estimation, a value of

12 -1

5x10 sec will be used. Tse, Welch, and Royce (1972a) report a

value of 0.78 eV for the enthalpy of motion of the F vacancy in

FAp, although they estimate (1972b) on theoretical grounds that Ah^

for the OH ion must be larger. We will use 0.78 eV, but must recognize

that for the OH ion motion may be slower and the ionic replacement

process therefore take longer than we estimate here. The entropy of

motion, As , is more difficult to estimate. However (c.f., Franklin, m

1972) in most ionic crystals As/k 1 to 3 for vacancy motion. We will

choose As k here.

With these values we find that at 380° C the mobility y is about

-7 2 2.8x10 cm /volt'sec at SSO^C, and the conductivity is about

—6 —1 —1

1.5x10 ohm cm . The time to completely exchange a crystal 1 cm

thick at this temperature would then be about 16 days.

This is a very crude estimate. The calculated replacement time is a

long but not impossible time. It may be a low estimate because of the
- 24 -

possibility that the mobility of OH ions is less than that of F ions.

On the other hand, somewhat higher temperatures should be possible, and

crystals only a tenth of a cm thick would still be suitable for most

physical property measurements.
- 25 -

REFERENCES

Ashton, F. W. and Wilson, R. , 1927, Am. J. Science l^, 209.

Baddiel, C. B. and Berry, E. E., 1966, Spectrochim. Acta 22_, 1407.

Bauerle, J. E., 1969, J. Phys. Chem. Sol. 2£, 2657.

Bernal, J. D. and Megaw, H. D., 1935, Proc. Roy. Soc. A151 , 384.

Buchanan, R. A., Caspers, H. H. , and Murphy, J., 1963, J. Appl. Optics

2_, 1147.

Busing, W. R. and Levy, H. A., 1957, J. Chem. Phys. 26_, 563.

Cole, K. S. and Cole, R. H. , 1942, J. Chem. Phys. 1£, 98.

Donovan, B. and Angress, J. F., 1971, Lattice Vibrations , (Chapman

Hall, Ltd., London) p. 98.

Elleman, D. D. and Williams, D. , 1956, J. Chem. Phys. 25_, 742.

Franklin, A. D. , 1972, in Point Defects in Solids , J. H. Crawford, Jr.

and L. M. Slifkin, Ed. (Plenum Press, N.Y.) p. 76.

Fripiat, J. J., Bosmans, H. , and Rouxhet, P. G., 1967, J. Phys. Chem.

71^, 1097.

Fripiat, J. J. and Touillaux, R. , 1969, Treins . Far. Soc. 65 , 1236.

Henderson, D. M. and Gutowsky, H. S., 1962, Am. Mineral. 47_, 1231.

Hoare, J. P., 1968, The Electrochemistry of Oxygen , (Interscience , New

York) p. 307.

Lidiard, A. B., 1957, Handbuch der Physik , Vol. 20, S. Flugge, Ed.,

(Springer-Verlag, Berlin) p. 246.

Mata Arjona, A. and Fripiat, J. J., 1967, Trans. Far. Soc. 63 , 2936.
- 26 -

Milligan, W. O. and McAtee, J. L., 1956, J. Phys. Chem. 60, 273.

Pimentel, G. C. and McClellan, A. L., 1960, The Hydrogen Bond

(Freeman, San Francisco) Fig. 3-9.

Prener, J. S., 1967, J. Electrochem. Soc. 114 , 77.

Raleigh, D. 0., 1968, J. Phys. Chem. Soc. £9, 261.

Schwartzmann, E., 1962, Z. Anorg. Chem. 317 , 176.

Tse, C, Welch, D. O. , and Royce, B. S. H., 1972a, Bull. Am. Phys. Soc.

Ser. II, r7, 265, Paper BH5; 1972b, Bull. Am. Phys. Soc, Ser. II,

17, 265, Paper BH4.

White, S., 1971, Nature 230 , 192.

Wickersheim, K. A. and Korpi, G. K. , 1965, J. Chem. Phys. 42, 579.
- 27 -

FIGURE CAPTIONS

1. Schematic diagram of cell for electrolytic conversion of FAp to

OHAp.

2. Schematic diagram for growth of CaCOH)^ crystals by diffusion.

3. Cell for ac electrical measurements of CaCOH)^ crystals.

4. Dependence of the shunt conductance of the electrical cell of

Figure 3 upon interelectrode spacing at three measurement frequencies.

The units of conductance are picosiemens (see footnote, p. 7)

5. Dependence of the shunt capacitance of the electrical cell of

Figure 3 upon interelectrode spacing at three measurement frequencies.

6. Dependence of the shunt capacitance and conductance of the electrical

cell of Figure 3 upon measurement frequency. The units of conductance

are picosiemens (see footnote, p. 7).

7. Frequency dependence of capacitance and conductance of Ca(0H)2

crystal 111-1 at 345 °C in all atmospheres. The units of conductance

are nanosiemens (see footnote, p. 7)

8. Frequency dependence of capacitance and conductance of Ca(0H)2

crystal 111-2 at 335°C in dry air. The units of conductance are

nanosiemens (see footnote, p. 7).
in

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30
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J

Fig. 4, Dependence of the shunt conductance of the electrical cell of

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frequencies. The units of conductance are picosiemens (see

footnote , p . 7)

Fig. 5. Dependence of the shunt capacitance of the electrical cell

of Figure 3 upon interelectrode spacing at three measurement

frequencies

31
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33

BIBLIOGRAPHIC DATA

! SHEET

1. Report No.

i NBSIR 73-404

2.

ulc .ii'.J Subtitle Mass Transport and Physical Properties of Large

jurystals of Calcium Apatites: Studies of Ca(0H)2 Crystals for

Jse in Electrolytic Conversion of Calcium Fluorapatite Crystals

o Calcium Hydroxyapatite

3.M<cclpicnt'.s Acccs.sion N(

5. Report Date j^^^ ^973

(Date of Issue)

6.

', .'\uthor(s1

1^. D. Franklin and K. F. Young

'i. Performing Organization Name and Address National Bureau of Standards

Department of Commerce

iJashington, D.C. 20234

Sponsoring Organization Name and Address 'ilational Institute of Dental Research

Sethesda, Md. 20014

8- Perforn:iing Organization Rcpt. No.

10. Ptoject/Task/Work Unit No. 3130457

11. Contract /Grant No. YOl-DE-30010

Formerly - NIDRIO

13. Type of Report & Period Covered

Annual, 9/72-8/73

14.

5. Supplementary Notes

6. Abstracts n order to convert single crystals of calcium fluorapatite to calcium hydroxyapatite,

;:n electrolytic cell technique will be explored. To utilize such a technique, the

liathode compartment must consist of a source of hydroxyl ions and a barrier to the flow

all others. Examination of the literature on metallic hydroxides suggests that a

'Tiitable cathode might be composed of an oriented Me(0H)2 crystal, where Me is Mg, Ca,

x, or Ba, backed up by a Pt electrode in an atmosphere containing H2O and O2 . Ca(0H)2

xystals have been grown from aqueous solution, and Pt electrodes evaporated onto them, r apparatus has been built to study their ac admittance as a function of temperature

nd atmosphere, and measurements begun. A computer program for handling the complex

dmittance data has been devised and tested.

Key Words and Document Analysis. 17a. Descriptors ac impedance; calcium apatites; calcium hydroxide; crystal growth; electrolysis;

interfacial polarization; ionic conduction; mass transport.

'b. Identifiers /Open-Ended Terms

:. COSATI Field/Group

Availability Statement 19. Security Class (This 21. No. of Pages

Report) 35

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